One of the first successful approaches to this was contained in the thesis of Brakke [1]}. In it, he
introduced a weak formulation, phrased in the geometric measure theoretic notion of varifolds. This is
a broad enough class to contain highly irregular objects, and mean curvature is defined in a distributional sense.
More precisely, a family of \(n\) -dimensional varifolds \(\lbrace V_t\rbrace _{t\in [0,T)}\)  is a solution of the Brakke flow if, for
almost every time, \(V_t\)  is an integral \(n\) –varifold with locally bounded first variation and generalized curvature
\(h\)  in \(L^2\)  such that for any compact set \(K\)  in \(\mathbb {R}^n\)  and \(t\in (0,T)\)  we have \(\sup _{\tau \in [0,t) }\Vert V_{\tau }\Vert (K)<\infty \) .
The flow is dictated by the requirement that for every function \(\phi \in {\mathcal {C}}^0(\mathbb {R}^{N} \times [0,T);\mathbb {R}^+)\) ,
we have
\(\frac{d\,}{dt} \int \phi (x, t)\, \mathrm {d}\Vert V_t\Vert \le \int \left( -\phi (x, t) h(V_t,x)^2 +\langle \nabla \phi , h(V_t,x)\rangle + (\partial _t \phi )(x, t)\right)\, \mathrm {d}\Vert V_t\Vert \,.\) 
